The objective in this work is to generate and discuss the stability results of fully-immersed end-milling process with parameters; tool mass m=0.0431kg,tool natural frequency ω_{n<\/sub> = 5700 rads^-1, damping factor ξ=0.002 and workpiece cutting coefficient C=3.5x10^7 Nm^-7\/4. Different no of teeth is considered for the end-milling. Both 1-DOF and 2-DOF chatter models of the system are generated on the basis of non-linear force law. Chatter stability analysis is carried out using a modified form (generalized for both 1-DOF and 2-DOF models) of recently developed method called Full-discretization. The full-immersion three tooth end-milling together with higher toothed end-milling processes has secondary Hopf bifurcation lobes (SHBL’s) that exhibit one turning (minimum) point each. Each of such SHBL is demarcated by its minimum point into two portions; (i) the Lower Spindle Speed Portion (LSSP) in which bifurcations occur in the right half portion of the unit circle centred at the origin of the complex plane and (ii) the Higher Spindle Speed Portion (HSSP) in which bifurcations occur in the left half portion of the unit circle. Comments are made regarding why bifurcation lobes should generally get bigger and more visible with increase in spindle speed and why flip bifurcation lobes (FBL’s) could be invisible in the low-speed stability chart but visible in the high-speed stability chart of the fully-immersed three-tooth miller.<\/p>\r\n","references":"[1]\tG. St\u00e9p\u00e1n, R. Szalai, and T. Insperger, \"Nonlinear Dynamics of High-Speed Milling Subjected to Regenerative Effect,\u201d in Nonlinear Dynamics of Production Systems, Gunther Radons, Ed. New York: Wiley-VCH, 2003, pp.1-2.\r\n[2]\tM.A. Davies, T. J. Burns and T. L. Schmitz, \"High-Speed Machining Processes: Dynamics of Multiple Scales,\u201d National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg MD 20899, USA, 1999.\r\n[3]\tT. Insperger, B.P. Mann, G. Stepan, and P.V. Bayly, \"Stability of up-milling and down-milling, part 1: alternative analytical methods,\u201d International Journal of Machine Tools and Manufacture vol. 43, 2003, pp. 25\u201334.\r\n[4]\tO. A. Bobrenkov , F. A. Khasawneh , E. A. Butcher, and B. P. Mann, \"Analysis of milling dynamics for simultaneously engaged cutting teeth,\u201d Journal of Sound and Vibration, vol 329, 2010, pp. 585\u2013606. \r\n[5]\tE. A. Butcher, H. Ma, E. Bueler, V. Averina, and Z. Szabo, \"Stability of linear time-periodic delay-differential equations via Chebyshev polynomials,\u201d International Journal for Numerical Methods in Engineering, vol. 59, 2004 pp. 895\u2013922.\r\n[6]\tT. Insperger, and G. Stepan, \"Semi-discretization method for delayed systems,\u201d International Journal For Numerical Methods In Engineering, vol. 55, 2002, pp. 503\u2013518.\r\n[7]\tT. Insperger, and G. Stepan, \"Stability of Milling Process,\u201d Periodica Polytechnica, vol. 44, no 1, 2000, pp. 47\u201357.\r\n[8]\tC. G. Ozoegwu, \"Chatter of Plastic Milling CNC Machine: Master of Engineering thesis,\u201d Nnamdi Azikiwe University Awka, 2011.\r\n[9]\tY. Ding, L.M. Zhu, X.J. Zhang and H. Ding, \"A full-discretization method for prediction of milling stability,\" International Journal of Machine Tools and Manufacture vol. 50, 2010, pp. 502\u2013509.\r\n[10]\tT. Insperger, \"Stability Analysis of Periodic Delay-Differential Equations Modelling Machine Tool Chatter: PhD dissertation,\u201d Budapest University of Technology and Economics, 2002.\r\n[11]\tT. Insperger, \"Full-discretization and semi-discretization for milling stability prediction: Some comments,\u201d International Journal of Machine Tools and Manufacture vol. 50, 2010, pp. 658\u2013662.\r\n[12]\tE. Butcher, and B. P. Mann, \"Stability Analysis and Control of Linear Periodic Delayed Systems using Chebyshev and Temporal Finite Element Methods,\u201d http:\/\/mae.nmsu.edu\/faculty\/eab\/ bookchapter_final.pdf. \r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 75, 2013"}}